Problem: The equation of a circle $C$ is $x^2+y^2-10x+18y+102 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Solution: To find the equation in standard form, complete the square. $(x^2-10x) + (y^2+18y) = -102$ $(x^2-10x+25) + (y^2+18y+81) = -102 + 25 + 81$ $(x-5)^{2} + (y+9)^{2} = 4 = 2^2$ Thus, $(h, k) = (5, -9)$ and $r = 2$.